0=14u^2+32u-u^3

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Solution for 0=14u^2+32u-u^3 equation: 


Simplifying
0 = 14u2 + 32u + -1u3

Reorder the terms:
0 = 32u + 14u2 + -1u3

Solving
0 = 32u + 14u2 + -1u3

Solving for variable 'u'.
Remove the zero:
-32u + -14u2 + u3 = 32u + 14u2 + -1u3 + -32u + -14u2 + u3

Reorder the terms:
-32u + -14u2 + u3 = 32u + -32u + 14u2 + -14u2 + -1u3 + u3

Combine like terms: 32u + -32u = 0
-32u + -14u2 + u3 = 0 + 14u2 + -14u2 + -1u3 + u3
-32u + -14u2 + u3 = 14u2 + -14u2 + -1u3 + u3

Combine like terms: 14u2 + -14u2 = 0
-32u + -14u2 + u3 = 0 + -1u3 + u3
-32u + -14u2 + u3 = -1u3 + u3

Combine like terms: -1u3 + u3 = 0
-32u + -14u2 + u3 = 0

Factor out the Greatest Common Factor (GCF), 'u'.
u(-32 + -14u + u2) = 0

Factor a trinomial.
u((-2 + -1u)(16 + -1u)) = 0


Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

Move all terms containing u to the left, all other terms to the right.

Simplifying
u = 0

Subproblem 2
Set the factor '(-2 + -1u)' equal to zero and attempt to solve:

Simplifying
-2 + -1u = 0

Solving
-2 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1u = 0 + 2
-1u = 0 + 2

Combine like terms: 0 + 2 = 2
-1u = 2

Divide each side by '-1'.
u = -2

Simplifying
u = -2

Subproblem 3
Set the factor '(16 + -1u)' equal to zero and attempt to solve:

Simplifying
16 + -1u = 0

Solving
16 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + -1u = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1u = 0 + -16
-1u = 0 + -16

Combine like terms: 0 + -16 = -16
-1u = -16

Divide each side by '-1'.
u = 16

Simplifying
u = 16
Solution
u = {0, -2, 16}

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